mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

 2017-06-03 
As a child, I was a huge fan of Captain Scarlet and the Mysterons, Gerry Anderson's puppet-starring sci-fi series. Set in 2068, the series follows Captain Scarlet and the other members of Spectrum as they attempt to protect Earth from the Mysterons. One of my favourite episodes of the series is the third: Big Ben Strikes Again.
In this episode, the Mysterons threaten to destroy London. They do this by hijacking a vehicle carrying a nuclear device, and driving it to a car park. In the car park, the driver of the vehicle wakes up and turns the radio on. Then something weird happens: Big Ben strikes thirteen!
The driver turning on the radio. Good to know that BBC Radio 4 will still broadcast at 92-95FM in 2068.
Following this, the driver is knocked out again and wakes up in a side road somewhere. After hearing his story, Captain Blue works out that the car park must be 1500 yards away from Big Ben. Using this information, Captains Blue and Scarlet manage to track down the nuclear device and save the day.
A map of London with a circle of radius 1500 yards drawn on it.
After rewatching the episode recently, I realised that it would be possible to recreate this scene and hear Big Ben striking thirteen.

Where does Big Ben strike thirteen?

At the end of the episode, Captain Blue explains to Captain Scarlet that the effect was due to light travelling faster than sound: as the driver had the radio on, he could hear Ben's bongs both from the tower and through the radio. As radio waves travel faster than sound, the bongs over the radio can be heard earlier than the sound waves travelling through the air. Further from the tower, the gap between when the two bongs are heard is longer; and at just the right distance, the second bong on the radio will be heard at the same time as the first bong from the tower. This leads to the appearance of thirteen bongs: the first bong is just from the radio, the next eleven are both radio and from the tower, and the final bong is only from the tower.
Big Ben's bongs are approximately 4.2s apart, sound travels at 343m/s, and light travels at 3×108m/s (this is so fast that it could be assumed that the radio waves arrive instantly without changing the answer). Using these, we perform the following calculation:
$$\text{time difference} = \text{time for sound to arrive}-\text{time for light to arrive}$$ $$=\frac{\text{distance}}{\text{speed of sound}}-\frac{\text{distance}}{\text{speed of light}}$$ $$=\text{distance}\times\left(\frac1{\text{speed of sound}}-\frac1{\text{speed of light}}\right)$$ $$\text{distance}=\text{time difference}\div\left(\frac1{\text{speed of sound}}-\frac1{\text{speed of light}}\right)$$ $$=4.2\div\left(\frac1{343}-\frac1{3\times10^8}\right)$$ $$=1440\text{m}\text{ or }1574\text{ yards}$$
This is close to Captain Blue's calculation of 1500 yards (and to be fair to the Captain, he had to calculate it in his head in a few seconds). Plotting a circle of this radius centred at Big Ben gives the points where it may be possible to hear 13 bongs.
Again, the makers of Captain Scarlet got this right: their circle shown earlier is a very similar size to this one. To demonstrate that this does work (and with a little help from TD and her camera), I made the following video yesterday near Vauxhall station. I recommend using earphones to watch it as the later bongs are quite faint.

Similar posts

Proving a conjecture
Mathsteroids
Building MENACEs for other games
Tube map kaleidocycles

Comments

Comments in green were written by me. Comments in blue were not written by me.
@g0mrb: Thanks for letting me know, I'll look into it...
Matthew
                 Reply
There is no sound in this video, using Safari in iOS 12.1.1 Beta.
g0mrb
                 Reply
This is awesome and wonderful. I salute you.
Ben Sparks
×1                 Reply
Wow! This has made my weekend.
Tony Mann
×1                 Reply
 Add a Comment 


I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li>
To prove you are not a spam bot, please type "e" then "q" then "u" then "a" then "t" then "i" then "o" then "n" in the box below (case sensitive):

Archive

Show me a random blog post
 2020 

Feb 2020

PhD thesis, chapter ∞
PhD thesis, chapter 5
PhD thesis, chapter 4
PhD thesis, chapter 3
Inverting a matrix
PhD thesis, chapter 2

Jan 2020

PhD thesis, chapter 1
Gaussian elimination
Matrix multiplication
Christmas (2019) is over
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

christmas national lottery go finite element method triangles curvature talking maths in public speed dataset matrices draughts frobel fractals chalkdust magazine harriss spiral accuracy golden spiral dates trigonometry weak imposition hats royal institution game of life programming manchester science festival geometry mathsjam video games binary pythagoras palindromes raspberry pi data visualisation radio 4 ternary chess computational complexity advent calendar signorini conditions sobolev spaces weather station machine learning matrix of cofactors interpolation chebyshev bempp statistics cross stitch boundary element methods platonic solids game show probability polynomials python menace royal baby electromagnetic field people maths hexapawn pizza cutting reddit countdown probability realhats phd final fantasy bubble bobble cambridge tennis inline code sport folding tube maps reuleaux polygons games captain scarlet mathsteroids plastic ratio matt parker latex gaussian elimination sound bodmas pac-man tmip puzzles determinants the aperiodical matrix multiplication european cup dragon curves map projections oeis numerical analysis matrix of minors london underground graph theory estimation world cup london mathslogicbot a gamut of games approximation misleading statistics books wool light flexagons stickers braiding simultaneous equations preconditioning folding paper craft football golden ratio coins asteroids hannah fry error bars propositional calculus inverse matrices data martin gardner news wave scattering big internet math-off noughts and crosses rugby javascript twitter gerry anderson php christmas card ucl manchester rhombicuboctahedron arithmetic sorting nine men's morris logic

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2020